Yes, the procedure works on both editions.
I understand the space thing.
Another option would be IMAPSYNC, but you'd loose some stuff, like documents. So, we probably should do the tar /opt/zimbra thing.
Lookup how to use rsync
man rsync
You can also just rsync the /opt/zimbra folder to the new server.
it's really up to you, but everything is contained in /opt/zimbra |